Question

List these three types of radiation-infrared, X-ray, and radio waves-in order of: (a) increasing energy per photon (b) increasing frequency (c) increasing wavelength

Short answer

The order by (a) increasing energy per photon is radio waves, infrared, X-rays; (b) increasing frequency is the same as energy, which is radio waves, infrared, X-rays; (c) increasing wavelength is X-rays, infrared, radio waves.

Step-by-step solution

- Understanding the Electromagnetic Spectrum

Recognize that infrared, X-ray, and radio waves are all forms of electromagnetic radiation which differ in energy, frequency, and wavelength. The energy per photon is directly proportional to the frequency and inversely proportional to the wavelength. This means that higher frequency (or lower wavelength) corresponds to higher energy per photon. The electromagnetic spectrum ranges from high-energy photons (like gamma rays) to low-energy photons (like radio waves).

- Ordering by Increasing Energy per Photon

Since X-rays have a higher frequency than infrared and radio waves, they have more energy per photon. Infrared has more energy per photon than radio waves. Thus, the order from lowest to highest energy per photon is: radio waves, infrared, X-rays.

- Ordering by Increasing Frequency

Frequency is highest for X-rays, followed by infrared, and lowest for radio waves. The order from lowest to highest frequency is: radio waves, infrared, X-rays.

- Ordering by Increasing Wavelength

Wavelength is inversely proportional to frequency. Hence, radio waves have the longest wavelength, followed by infrared, and X-rays have the shortest. The order from shortest to longest wavelength is: X-rays, infrared, radio waves.

Key concepts

Energy Per Photon

Understanding the energy of individual photons is fundamental to grasping various concepts in physics and chemistry, particularly in the study of the electromagnetic spectrum. Each photon carries a quantized amount of energy, which is directly related to the radiation's frequency. The higher the frequency, the more energy each photon contains.

The formula that defines the energy (\( E \) in joules) of an individual photon is given by Planck's equation: \[ E = hf \] where \( h \) is Planck's constant (\( 6.626 x 10^{-34} Js \) ) and \( f \) is the frequency of the photon in hertz. As a rule of thumb, photons of visible light have more energy than those of radio waves but less energy than X-rays, placing visible light somewhere in the middle of the electromagnetic spectrum regarding photon energy.

In the exercise, we discern that X-rays have the highest energy per photon, followed by infrared and lastly, radio waves. This is because of their respective place in the electromagnetic spectrum, with X-rays having higher frequencies, infrared lower, and radio waves even lower still. Knowing the energy carried by photons is crucial in applications such as medical imaging, where high-energy X-rays are used to penetrate tissues, and in communications, where lower-energy radio waves are utilized for long-distance signal transmission.

Electromagnetic Radiation Types

Electromagnetic radiation is a form of energy that is all around us and takes various forms, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. These forms are distinguished by their different wavelengths and frequencies, and they make up the electromagnetic spectrum.

Radio Waves

Used in broadcasting and communication, radio waves have the lowest frequencies and longest wavelengths in the electromagnetic spectrum.

Infrared

Warm objects emit infrared radiation, which is just beyond the visible spectrum and can be felt as heat.

X-rays

Due to their high energy, X-rays can penetrate materials and are commonly used in medical imaging.

Each type of electromagnetic radiation interacts with matter differently, which defines its range of applications. For instance, ultraviolet light can cause chemical reactions, visible light is the range in which our eyes are sensitive, and gamma rays are used in cancer treatment due to their high energy capable of damaging cells. When addressing electromagnetic radiation types, it is essential to focus on how their differences in energy and wavelength dictate their use in everyday life and scientific applications.

Wavelength and Frequency Relationship

The wavelength and frequency of electromagnetic radiation are inversely related and determine the nature of the various types of radiation observed across the electromagnetic spectrum. This relationship is crucial in both natural phenomena and technological applications.

The mathematical expression of this relationship is given by the equation: \[ c = \lambda f \] where \( c \) is the speed of light in a vacuum, \( \lambda \) (lambda) is the wavelength in meters, and \( f \) is the frequency in hertz. Since the speed of light is constant in a vacuum (\( 3.00 x 10^8 m/s \)), an increase in frequency leads to a decrease in wavelength, and vice versa.

In the context of the exercise, understanding this relationship helps us arrange the types of radiation in order. Since radio waves have the longest wavelength, they must have the lowest frequency, and X-rays, with their short wavelengths, have high frequencies. This inverse relationship is not only theoretical but practical; for instance, when tuning a radio, changing the frequency (and thus the wavelength) leads to different radio stations being received. Similarly, the colors we perceive are due to visible light of different wavelengths, which correspondingly have distinct frequencies.